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In this paper, we propose a multiplex proportional-integral approach, forsolving consensus problems in networks of heterogeneous nodes dynamics affectedby constant disturbances. The proportional and integral actions are deployed ontwo different layers across the network, each with its own topology. Sufficientconditions for convergence are derived that depend upon the structure of thenetwork, the parameters characterizing the control layers and the nodedynamics. The effectiveness of the theoretical results is illustrated using apower network model as a representative example.

Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents